system identification using adaptive filter algorithms - IOSR journals

IOSR Journal of Electronicsl and Communication Engineering (IOSR-JECE) ISSN: 2278-2834-, ISBN: 2278-8735, PP: 54-59 www.iosrjournals.org

SYSTEM IDENTIFICATION USING ADAPTIVE FILTER ALGORITHMS S.D.Shinde1, Mrs.A.P.Patil2,Mrs.P.P.Belagali3 1(

Dept. of Electronics & Telecommunication Engg, JJMCOE Jaysingpur, India.) 2,3( Dept. of Electronics Engg, JJMCOE Jaysingpur, India.)

ABSTRACT— Anew framework for designing robust adaptive filters is introduced. It is based on the optimization of a certain cost function subject to a time-dependent constraint on the norm of the filter update. Particularly, we present a robust variable step-size NLMS algorithm which optimizes the square of the a posteriori error. We also show the link between the proposed algorithm and another one derived using a robust statistics approach. In addition, a theoretical model for predicting the transient and steady-state behavior and a proof of almost sure filter convergence are provided. The algorithm is then tested in different environments for system identification and acoustic echo cancelation applications. INDEX TERMS—Acoustic echo cancelation, adaptive filtering, impulsive noise, normalized least-meansquare (NLMS) algorithm, robust filtering.

I. INTRODUCTION A least mean squares (LMS) filter is an adaptive filter that adjusts its transfer function according to an optimizing algorithm. You provide the filter with an example of the desired output together with the input signal. The filter then calculates the filter weights, or coefficients, that produce the least mean squares of the error between the output signal and the desired signal. To improve the convergence performance of the LMS algorithm, the normalized variant (NLMS) uses an adaptive step size based on the signal power. As the input signal power changes, the algorithm calculates the input power and adjusts the step size to maintain an appropriate value. Thus the step size changes with time. As a result, the normalized algorithm converges more quickly with fewer samples in many cases. For input signals that change slowly over time, the normalized LMS can represent a more efficient LMS approach.

II. GENERALIZED BLOCK DIAGRAM

UNKNOWN SYSTEM (FIR FILTER)

x(k) d(k) ADAPTIVE FILTER (FIR FILTER)

y(k )

+ -

n(k )

e(k)

ADAPTATION ALGORITHM

Block Diagram for System Identification Second International Conference on Emerging Trends in engineering (SICETE) Dr. J.J. Magdum College of Engineering, Jaysingpur

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SYSTEM IDENTIFICATION USING ADAPTIVE FILTER ALGORITHMS III. LEAST MEAN SQUARE ALGORITHM LMS algorithm uses the estimates of the gradient vector from the available data. LMS incorporates an iterative procedure that makes successive corrections to the weight vector in the direction of the negative of the gradient vector which eventually leads to the minimum mean square error. Compared to other algorithms LMS algorithm is relatively simple; it does not require correlation function calculation nor does it require matrix inversions. LMS algorithms have a step size that determines the amount of correction to apply as the filter adapts from one iteration to the next. Choosing the appropriate step size requires experience in adaptive filter design. Filter convergence is the process where the error signal (the difference between the output signal and the desired signal) approaches an equilibrium state over time The LMS algorithm initiated with some arbitrary value for the weight vector is seen to converge and stay stable for 0 < μ < 1/λmax Where λmax is the largest eigenvalue of the correlation matrix R. The convergence of the algorithm is inversely proportional to the eigenvalue spread of the correlation matrix R. When the eigenvalues of R are widespread, convergence may be slow. The eigenvalue spread of the correlation matrix is estimated by computing the ratio of the largest eigenvalue to the smallest eigenvalue of the matrix. If μ is chosen to be very small then the algorithm converges very slowly. A large value of μ may lead to a faster convergence but may be less stable around the minimum value. One of the literatures [will provide reference number here] also provides an upper bound for μ based on several approximations as μ